Be very careful with any camping and guns combination on public land. Check the park websites for where you are going, and call the local ranger office to get the final word.
I've lived in FL, NC, and GA, and it's not legal to target practice or "plink" in the state/national parks in any of those states.
Park Rangers can and will search your campsite, it's just not worth it.
Find out what the law requires, and follow it.